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First of all the workings of REGE are not all together clear and you may be
attributing an accuracy to the results beyond what is there. In particular
the three iterations is left over from the days when computing these values
was very slow. You may get rather different results if you increase from the
three iterations. However, let us assume that what you have done is correct
and the partitions do indeed reflect regular equivalence classes.

At the first stage you do not give any information about the relationships
between the groups you find and the rest of the network. From a structural
point of view these positions must be significant but at the same time you
indicate they are marginal.

Suppose this was a friendship network and the values of the links represented
strength of friendship. If one group have  weak links to an individual and
another group have say no links to the same individual and further suppose
the groups have stronger internal ties and stronger ties to each other
(across the groups) than to the outsider. Then REGE will focus on the
structural properties of the outsider and place the outsider in a single
group before looking at the differences in the two groups. It will then find
the two groups because of their different relationship with the outsider. But
these two groups may not be two groups since they only have weak links to the
outsider. Since REGE does not rank strength but looks for similarity of ties
then it has formed the groups on very weak evidence. In this case it is quite
legitimate to remove the outsider and look for the structure which represents
the patterning without the excluded individual.

In other words what you do is completely justifiable provided the groups you
remove are really marginal and not just inconvenient. 

In essence you need to determine if these nodes are really peripheral and if
they are then you are OK. If they are not then you really should not do this.


Martin Everett

-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Carl Nordlund
Sent: 22 May 2007 15:29
To: [log in to unmask]
Subject: Arbitrary removal of nodes in reg eq-analysis?

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Hi all,
Having a little dilemma here which I guess others before me have 
confronted. Being self-taught in everything SNA, I pose my question to 
this email list, hoping for some tutoring on the subject!

I'm currently doing a reg. equivalence analysis on energy flows (energy 
content in four fuel commodities) between the countries of the world - 
data is valued, directional with quite a large value span among the flow 
values. Using the REGE-algorithm in the Ucinet package, 3 iterations, 
selecting the number of partitions based on an Anova Density check for 
different number of partitions (as used in Luczkovich et al).

When using 99 countries in my dataset, I get an optimal split at 11 
partitions (i.e. positions containing role-equivalent actors). Two of 
these are singleton positions, i.e. containing only singular countries, 
and two positions contain only two countries each. All these 6 countries 
are fairly small and uninteresting, covering only 0.27% of total world 
population, 0.04% of total world GDP, and 0.03% of total flow values in 
the dataset.

Thus, what I would like to do is to remove these 6 countries from my 
dataset and repeat the analysis with only 93 countries. When doing so, I 
get an optimal number of positions at 8, the two smallest of these 
positions containing 3 and 4 countries respectively. I find this 1) much 
easier to analyze, 2) much easier to visualize (as a reduced/image 
graph), 3) giving a higher resolution (more partitions) regarding the 
positions containing the bulk of countries, and 4) removing countries 
that I feel could "disturb" the REGE algorithm in finding the major 
positions, removing countries that though might be unique but not very 
significant with respect to their coverage (as given by share of total 
flow values and attributional measures such as population and GDP).

However: how on earth can I motivate this? Can I just simply argue that 
"well, first I included these 6 countries, but as these countries 
resultet in 4 unique positions containing only these countries, I chose 
to remove these countries from the dataset and try without them - they 
are so small and insignificant anyhow..."? I could probably find some 
criteria for removing these based on their attributes, net degrees or 
similar, but that would not be very scientifically honest now, would it?

How have other people done in analyses that yields a bunch of trivial 
and singleton positions, i.e. positions that only contain 1-2 actors 
that are of fairly minor importance anyway? Suggestions?

(And sorry for using this email list as a classroom here - I have 
nowhere else to turn to...)


Carl Nordlund, BA, PhD student
Human Ecology Division, Lund university

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